The graph-based geometric constraint solving technique works in two steps. First the geometric problem is translated into a
graph whose vertices represent the set of geometric elements and whose edges are the constraints. Then the constraint
problem is solved by decomposing the graph into a collection
of subgraphs each representing a standard problem which is
solved by a dedicated equational solver.
In this work we report on an algorithm to decompose biconnected
tree-decomposable graphs representing either underor
wellconstrained 2D geometric constraint problems. The
algorithm recursively first computes a set of fundamental
circuits in the graph then splits the graph into a set of
subgraphs each sharing exactly three vertices with the fundamental
circuit. Practical experiments show that the reported
algorithm clearly outperforms the treedecomposition
approach based on identifying subgraphs by applying specific
decomposition rules.